Coronavirus Containment Corps Act This bill requires the Centers for Disease Control and Prevention (CDC) to develop, within 21 days, a nationwide contact tracing strategy for COVID-19 (i.e., coronavirus disease 2019) that addresses issues including workforce needs. To implement that strategy, the bill establishes grant programs in the CDC and the Indian Health Service (IHS). It also expands programs in the Department of Labor. The CDC must award grants to state and local health departments to, among other purposes, hire and train individuals for contact tracing positions and related roles. The IHS must award similar grants to tribes and tribal organizations. Additionally, Labor must award grants for states and other jurisdictions to support recruitment and employment of dislocated workers and other individuals in public health roles. Grants and contracts that include contact tracing in their scope of work must comply with prevailing wage requirements that apply to federal service contracts. Employees who work under such grants or contracts must receive similar compensation to that prevailing in the locality where work is performed. The CDC and Labor must report certain information on specified timelines, and the Government Accountability Office must evaluate the activities of grantees.